On the locked dynamical states of an overdamped Josephson junction array

Abstract

We study the dynamics of a 2D array of Josephson junctions biased with both dc and ac currents. Within certain ranges of the dc current intensity a locking between the natural oscillation frequency of the array and that of the ac forcing term occurs, giving rise to periodic solutions. As expected, a set of Shapiro steps appears in the curve. We show that there is no one-to-one correspondence between the value of on the Shapiro step and the dynamical state of the array. In particular for a frustration equal to 0.5, besides the well-known ground state, g.s., of the array (the checkerboard-like vortex configuration), there exist other dynamical states accessible to the system. These latter are characterized by the same average voltage of the g.s. but different average energies and vortex configurations, with one or more domain walls. These `new' states are stable against small thermal fluctuations and phase perturbations. A better insight into the physical conditions needed to generate them has been obtained by studying the dynamical behaviour of a ladder as a function of its size and of its orientation with respect to the external bias current The relevance of our observations to the experimental studies of the array dynamics performed on a microscopical scale is briefly discussed.